Fast and Accuracy-Preserving Domain Decomposition Methods for Reduced Fracture Models with Nonconforming Time Grids
Fast and Accuracy-Preserving Domain Decomposition Methods for Reduced Fracture Models with Nonconforming Time Grids
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DOI：
10.1007/s10915-023-02251-0
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发表时间：
2023-05
影响因子：
2.5
通讯作者：
P. Huynh;Yanzhao Cao;Thi-Thao-Phuong Hoang
中科院分区：
文献类型：
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作者：
P. Huynh;Yanzhao Cao;Thi-Thao-Phuong Hoang
本文研究了裂隙多孔介质中可压缩流体流动的数值解。裂缝代表一条快速通道（即高渗透率），并被建模为嵌入多孔介质中的超表面。我们的目标是为这种简化的裂缝模型开发快速收敛和精确的全局时域分解（DD）方法，其中裂缝中较小的时间步长可以与子域中较大的时间步长相耦合。以压力连续性方程和裂缝界面的切向偏微分方程为传输条件，推导出三种不同的DD公式；每种方法都会导致一个时空接口问题，该问题在时间上迭代地全局求解。设计了有效的预调节器，以加速迭代方法的收敛，同时在不一致网格下保持迭代方法的及时精度。针对非浸没裂缝和部分浸没裂缝的二维问题给出了数值结果，证明了所提方法的改进性能。
This paper is concerned with the numerical solution of compressible fluid flow in a fractured porous medium. The fracture represents a fast pathway (i.e., with high permeability) and is modeled as a hypersurface embedded in the porous medium. We aim to develop fast-convergent and accurate global-in-time domain decomposition (DD) methods for such a reduced fracture model, in which smaller time step sizes in the fracture can be coupled with larger time step sizes in the subdomains. Using the pressure continuity equation and the tangential PDEs in the fracture-interface as transmission conditions, three different DD formulations are derived; each method leads to a space-time interface problem which is solved iteratively and globally in time. Efficient preconditioners are designed to accelerate the convergence of the iterative methods while preserving the accuracy in time with nonconforming grids. Numerical results for two-dimensional problems with non-immersed and partially immersed fractures are presented to show the improved performance of the proposed methods.